Over the past five years, an Arlington company has become the fastest growing publicly held small business in the area -- in part by helping cities and states to unsnarl outmoded financial accounting systems.

As limited resources have thrown the problems of local government accounting into sharp relief, American Management Systems Inc.'s sales have grown at a rate of nearly 60 percent a year. The company also provides computer services to customers, including federal agencies and provides management consulting.

From 1975 to 1979, its sales grew from approximately $7.2 million to more than $46.8 million, according to Inc. magazine, which rated the company the 56th most rapidly expanding publicly held small business.

Among those customers in 1979 were the Financial Oversight Committee for the District of Columbia, the City of New York and the State of Illinois.

American Management Systems is designing the so-called Financial Management System for the District of Columbia, a computerized record-keeping setup designed to put the city's books in auditable form. According to a filing with the Securities and Exchange Commission, that contract alone accounted for nearly 12 percent of the firm's 1979 sales.

The company also designed a similar system for New York City that accounted for 10.9 percent of its sales, and it is developing a Medicaid management information system for the State of Illinois.

"When we founded American Management Systems in February 1970, our goal was to become a major firm in the computer services industry," said the company's officers in a 1979 report to stockholders. The company is now one of the 10 largest independent firms in the computer services industry, they said.

American Management Systems was founded by five Defense Department coworkers and grew to one of the largest companies in the Washington area. It employs approximately 1,000 workers in eight offices around the country, including New York City, Chicago and San Francisco.